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Results for “adiabatic invariant”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Secular-invariant relationships among internal geomagnetic field coefficients

Some features of the secular variation of the geomagnetic field are examined. Contours encircling constant magnetic flux (third adiabatic invariant), corresponding to a shell of field lines in secular motion, reveal a general westward drift that is longitude and latitude dependent (with minima in the north Pacific and south Atlantic areas). Some invariant relationships appear among the field coefficients in the tilted, centered dipole (geomagnetic) coordinate system.

Roederer, J. G.↗
DOE OSTI2022

Modification of the Loss Cone for Energetic Particles in the Earth's Inner Magnetosphere

The behavior of energetic particles in the Earth's dipole and stretched magnetic-field models is explored with a focus on the shift of the atmospheric loss cone away from the magnetic-field direction and on non-adiabatic behavior occurring when the particle gyroradius becomes comparable with the gradient scale length of the local magnetic field. It is shown that the equatorial loss cone is aberrated away from the magnetic-field direction (pitch angle of 0°) by the perpendicular drift of a charged particle (which is referred to as the “Mozer transform” described in Mozer (1966, https://doi.org/10.1029/JZ071i011p02701). It is found that the Mozer coordinate transformation in pitch-angle/gyrophase-angle space better organizes the behavior of bounce times, mirror altitudes, drift speeds, and first adiabatic invariant. It also describes the loss-cone shift accurately for a certain range of values of the adiabaticity parameter ϵ, defined by the ratio of the particle gyroradius to the local radius of curvature of the magnetic field. For particles with larger ϵ, the Mozer transform (evaluated with the standard gradient-curvature drift) breaks down and the “central trajectory” theory can be used to calculate the angular shift of the loss cone, which now includes an Earthward shift. When ϵ becomes relatively large, stochastic field line curvature (FLC) scattering occurs: we show the intimate connection between the strength of FLC scattering and the loss-cone shift. Finally, by comparing ion orbits in the dipole and Tsyganenko (Ts89 and Ts04) magnetic fields, we conclude that the loss cone of ring-current ions is significantly modified during geomagnetically active times.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Bounce-Averaged Hamiltonian for Charged Particles in an Axisymmetric but Nondipolar Model Magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗
NASA NTRS1992

On steady field-aligned double-adiabatic flow

The paper summarizes the four general double-adiabatic invariants governing ideal MHD flow in a narrow tube and renders them in a form suitable for the calculation of flow in tubes of nonconstant cross-sectional area. Results for converging-diverging flux tubes are developed and compared to single-adiabatic results which are identical to those for ordinary gasdynamic flow. It is found that in certain parameter regimes the governing equation for the vector potential is elliptic and can be reduced to Laplace's equation by simple stretching of one coordinate. In other regimes the equation is hyperbolic, indicating the presence of wave patterns. The relevance of these results to flow over magnetopause undulations, including flux transfer events, is discussed.

Sonnerup, B. U. O.↗
NASA NTRS1983

On the equation of state of solar wind ions derived from Helios measurements

The radial evolution of such adiabatic invariants as the ion magnetic moments are studied on the basis of solar wind ion velocity distribution observations made by the Helios spacecraft between 0.3 and 1 AU. Significant differences between proton and alpha-particle parameters in wind velocity dependence are noted, and adiabaticity is on the average found to be violated. This violation is interpreted as evidence that protons are heated perpendicular to the field in fast streams. The contribution of the differential streaming energy to the total internal energy of the ions is also considered, and average heliocentric radial profiles for the ion heat fluxes are presented together with an examination of a possible ion heat flux role in the supply of thermal energy during the winds radial expansion. The present findings suggest that wave-particle interactions, and/or Coulomb collisions, are required to explain solar wind ion thermal energy states and radial temperature profiles.

Marsch, E.↗
NASA NTRS2013

Computational Studies of Magnetic Nozzle Performance

An extensive literature review of magnetic nozzle research has been performed, examining previous work, as well as a review of fundamental principles. This has allow us to catalog all basic physical mechanisms which we believe underlie the thrust generation process. Energy conversion mechanisms include the approximate conservation of the magnetic moment adiabatic invariant, generalized hall and thermoelectric acceleration, swirl acceleration, thermal energy transformation into directed kinetic energy, and Joule heating. Momentum transfer results from the interaction of the applied magnetic field with currents induced in the plasma plume., while plasma detachment mechanisms include resistive diffusion, recombination and charge exchange collisions, magnetic reconnection, loss of adiabaticity, inertial forces, current closure, and self-field detachment. We have performed a preliminary study of Hall effects on magnetic nozzle jets with weak guiding magnetic fields and weak expansions (p(sub jet) approx. = P(sub background)). The conclusion from this study is that the Hall effect creates an azimuthal rotation of the plasma jet and, more generally, creates helical structures in the induced current, velocity field, and magnetic fields. We have studied plasma jet expansion to near vacuum without a guiding magnetic field, and are presently including a guiding magnetic field using a resistive MHD solver. This research is progressing toward the implementation of a full generalized Ohm's law solver. In our paper, we will summarize the basic principle, as well as the literature survey and briefly review our previous results. Our most recent results at the time of submittal will also be included. Efforts are currently underway to construct an experiment at the University of Michigan Plasmadynamics and Electric Propulsion Laboratory (PEPL) to study magnetic nozzle physics for a RF-thruster. Our computational study will work directly with this experiment to validate the numerical model, in order to study magnetic nozzle physics and optimize magnetic nozzle design. Preliminary results from the PEPL experiment will also be presented.

Ebersohn, Frans H.↗
DOE OSTI2021

Normal stability of slow manifolds in nearly periodic Hamiltonian systems

Kruskal [J. Math. Phys. 3, 806 (1962)] showed that each nearly periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly invariant manifolds of each order, near which rapid oscillations are suppressed. We study the nonlinear normal stability of these slow manifolds for nearly periodic Hamiltonian systems on barely symplectic manifolds—manifolds equipped with closed, non-degenerate 2-forms that may be degenerate to leading order. In particular, we establish a sufficient condition for long-term normal stability based on second derivatives of the well-known adiabatic invariant. We use these results to investigate the problem of embedding guiding center dynamics of a magnetized charged particle as a slow manifold in a nearly periodic system. Here, we prove that one previous embedding and two new embeddings enjoy long-term normal stability and thereby strengthen the theoretical justification for these models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Axion dark matter from frictional misalignment

We study the impact of sphaleron-induced thermal friction on the axion dark-matter abundance due to the interaction of an axion-like particle (ALP) with a dark non-abelian gauge sector in a secluded thermal bath. Thermal friction can either enhance the axion relic density by delaying the onset of oscillations or suppress it by damping them. We derive an analytical formula for the frictional adiabatic invariant, which remains constant along the axion evolution and which allows us to compute the axion relic density in a general set-up. Even in the most minimal scenario, in which a single gauge group is responsible for both the generation of the ALP mass and the friction force, we find that the resulting dark-matter abundance from the misalignment mechanism deviates from the standard scenario for axion masses m a ≳ 100 eV. We also generalize our analysis to the case where the gauge field that induces friction and the gauge sector responsible for the ALP mass are distinct and their couplings to the axion have a large hierarchy as can be justified by means of alignment or clockwork scenarios. We find that it is easy to open up the ALP parameter space where the resulting axion abundance matches the observed dark-matter relic density both in the traditionally over- and underabundant regimes. This conclusion also holds for the QCD axion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Verification of nonperturbative guiding center theory in symmetric fields

We verify a recently-developed nonperturbative guiding center formalism to charged particle dynamics in fields with two-parameter continuous symmetry groups. This entails finding exact constants of motion, valid in the nonperturbative regime, that agree with Kruskal’s adiabatic invariant series to all orders in the perturbative regime, when the field scale length is large compared with a typical gyroradius. We demonstrate that the nonperturbative guiding center model makes exact predictions in these cases, even though it eliminates the cyclotron timescale, thereby establishing a theoretical baseline for performance of the nonperturbative formalism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Finite orbit width effects in large aspect ratio stellarators

New orbit-averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity-space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS (Velasco et al. , J. Comput. Phys. , vol. 418, 2020, 109512; Velasco et al. , Nucl. Fusion , vol. 61, 2021, 116013). The equations are used to study the $1/\nu$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/\nu$ regime transitions directly into the $\nu$ regime, without passing through a $\sqrt {\nu }$ regime. An explicit formula for the neoclassical fluxes in the $\nu$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrt {\nu }$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by Calvo et al. ( Plasma Phys. Control. Fusion , vol. 59, 2017, 055014). In these stellarators, the $\sqrt {\nu }$ regime exists in the collisionality interval $(a/R) \ln (R/a) \ll \nu _{ii} R a/\rho _i v_{ti} \ll R/a$ . In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrt {\nu }$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $\delta$ : $\delta ^{2} |\ln \delta | \ll \nu _{ii} R a/\rho _i v_{ti} \ll 1$ . Here, $\nu _{ii}$ is the ion–ion collision frequency, $\rho _i$ and $v_{ti}$ are the ion gyroradius and thermal speed, and $a$ and $R$ are the minor and major radii.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Electron kinetics in a high- Z plasmoid

The problem of the electron dynamics on a closed magnetic field line passing through a high-Z plasmoid is considered. The electron kinetic equation is integrated over bounce motion and pitch angle, reducing the independent variables to a single adiabatic invariant plus time. Integration of the full Landau self-collision operator is carried out exactly, resulting in a nonlinear integro-differential operator in the new invariant. Conservation laws and the H theorem of the integrated self-collision operator are proven. Numerical solutions of the integrated kinetic equation are obtained with a self-consistent quasineutral electric potential, given the initial condition of a cold plasmoid immersed in a hot ambient plasma. The fact that cold electrons are deeply trapped in a potential with a parabolic peak leads to exactly 3/4 the usual rate of collisional heating by the ambient plasma, independent of any other parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Is there an exact magnetic moment for charged particle motion in a time-dependent, homogeneous magnetic field?

The non-perturbative guiding-centre model provides an exact alternative to full-orbit simulations of charged particle dynamics in situations where traditional guiding-centre theory may fail. We demonstrate that the charged particle motion in a homogeneous, time-varying magnetic field is a solvable example of the non-perturbative guiding-centre model. This entails showing that the exact magnetic moment of Qin and Davidson can be constructed to be asymptotic to the adiabatic invariant series of Kruskal. In contrast to the perturbative invariant, the exact invariant contains information about parametric resonances. These resonances destroy the conservation of the usual magnetic moment over very long times. This refutes some previous claims about the all-time invariance of the magnetic moment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Modeling the Effects of Drift Orbit Bifurcation on Radiation Belt Electrons

Abstract Drift orbit bifurcation (DOB) has been suggested to play a major role in the loss and transport of radiation belt electrons since it violates the second adiabatic invariants of particles and makes the third invariant undefined. Results from our guiding‐center test particle simulations using the Tsyganenko‐1989c magnetic field model show that the DOB could affect a broad region of the outer radiation belt, which can penetrate inside the geosynchronous orbit at Kp ≥ 3, and its effects are more significant further away from the Earth, at a higher Kp and for higher electron energies. Specifically, the short‐term simulation results after one electron drift show both traditional and nontraditional DOB transport of electrons, with the nontraditional DOB, caused by a third minimum of the magnetic field strength near the equator, reported here for the first time. Moreover, our results show large ballistic jumps in the second invariant and radial distance for electrons at high equatorial pitch angles after one drift. In addition, long‐term DOB transport coefficients of electrons over many drifts are calculated based on our simulation results. We find that the pitch angle and radial diffusion coefficients of electrons due to DOB could be comparable to or even larger than those caused by electron interactions with chorus and Ultra‐Low‐Frequency waves, respectively. In sum, our results demonstrate that DOB could cause effective loss and transport of radiation belt electrons even in the absence of waves.

Astronomy & Astrophysics↗
DOE OSTI2024

Simulating Long–Term Dynamics of Radiation Belt Electrons Using DREAM3D Model

Here, we compared the performance of DREAM3D simulations in reproducing the long-term radiation belt dynamics observed by Van Allen Probes over the entire year of 2017 with various boundary conditions (BCs) and model inputs. Specifically, we investigated the effects of three different outer boundary conditions, two different low-energy boundary conditions for seed electrons, four different radial diffusion (RD) coefficients (DLL), four hiss wave models, and two chorus wave models from the literature. Using the outer boundary condition driven by GOES data, our benchmark simulation generally well reproduces the observed radiation belt dynamics inside L* = 6, with a better model performance at lower μ than higher μ, where μ is the first adiabatic invariant. By varying the boundary conditions and inputs, we find that: (a) The data-driven outer boundary condition is critical to the model performance, while adding in the data-driven seed population doesn't further improve the performance. (b) The model shows comparable performance with DLL from Brautigam and Albert (2000, https://doi.org/10.1029/1999ja900344), Ozeke et al. (2014, https://doi.org/10.1002/2013ja019204), and Liu et al. (2016, https://doi.org/10.1002/2015gl067398), while with DLL from Ali et al. (2016, https://doi.org/10.1002/2016ja023002) the model shows less RD compared to data. (c) The model performance is similar with data-based hiss models, but the results show faster loss is still needed inside the plasmasphere. (d) The model performs similarly with the two different chorus models, but better capturing the electron enhancement at higher μ using the Wang et al. (2019, https://doi.org/10.1029/2018ja026183) model due to its stronger wave power, since local heating for higher energy electrons is under-reproduced in the current model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Outer Radiation Belt Dynamics During the October 2012 Storm Revisited: Rapid Inward Radial Transport From a Dynamic Outer Boundary

Earth's outer radiation belt electron flux is highly variable and can be enhanced by over an order of magnitude over timescales less than one day, as observed during the October 2012 storm. Previous studies of this storm (e.g., Reeves et al., 2013, https://doi.org/10.1126/science.1237743) have invoked local acceleration to explain this. However, here, we argue that the observations can instead be explained by fast inward radial transport. One method often invoked to distinguish between these two acceleration processes is the existence of local peaks in electron phase space density (PSD) as a function of L* at fixed first, M, and second, K, adiabatic invariants. However, this method relies on the assumption that the evolution of the PSD as a function of L* occurs over timescales slower than the satellite orbital period. Here, high spatiotemporal resolution data from the Global Positioning System (GPS) spacecraft constellation is used to show that enhancements in the PSD occur during the October 2012 storm over short timescales not resolvable by the Van Allen Probes. In addition, Geostationary Operational Environmental Satellite spacecraft data also indicate that these enhancements are consistent with relativistic electron injections. A radial diffusion model is shown to reproduce the PSD dynamics observed by the Van Allen Probes, once rapid variations at the simulation outer boundary are included, consistent with GPS data. This verifies that apparently “locally growing” peaks in PSD along high apogee satellite orbits can be produced by fast inward radial transport without requiring the action of any local acceleration processes.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Collisionless adiabatic afterglow

In this work, we study, by numerical and analytical means, the evolution of a collisionless plasma initiated between absorbing walls. The ensuing flow is described by rarefaction waves that travel inward from the boundaries, interact, and eventually vanish after crossing through, leading up to the asymptotic stage of the decay. Particle simulations indicate that the kinetic evolution strongly resembles one found in isentropic gas dynamics. Namely, a very gradual density profile forms in the expanding central region where the rarefaction waves interact, with an accompanying linear velocity profile. Asymptotically, the density falls off as 1/t. The density and the flux at the boundary show little variation over the period when rarefaction waves still exist. Plasma potential, on the other hand, drops quite rapidly (on the underlying ion-acoustic timescale) to less than initial electron temperature Te when over 70% of the particles still remain in the system. This is due to electron kinetics being governed by conservation of adiabatic invariant in a slowly varying potential well. Analytical model of the velocity distribution is presented to explain the simulations. The results have implications for afterglow plasmas used in material processing and also for ion-extraction devices. One property of potential interest is good uniformity of the decaying plasma that occurs after approximately one ion-acoustic time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗